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Arithmetic Progression Worksheet for Olympiad

Maths Olympiad topic 29: Sequences and AP · Set 67 · 40 questions
TalentJR

How to solve it (Same step every time): In an AP the gap (common difference d) is always the same. nth term = a + (n − 1) × d, where a is the first term. Sum of n terms = n × (first + last) ÷ 2; so 1 + 2 + … + n = n × (n + 1) ÷ 2, and the first n odd numbers add up to n × n.

NameDateTime takenScore ___ / 40
  1. 1.What is the 40th term of the AP 17, 24, 31, 38, …? (a) 290 (b) 280 (c) 273 (d) 297
  2. 2.What is the sum of the first 7 terms of the AP 7, 8, 9, …? (a) 140 (b) 13 (c) 71 (d) 70
  3. 3.What is the sum of the first 5 terms of the AP 1, 4, 7, …? (a) 35 (b) 13 (c) 38 (d) 70
  4. 4.What is the missing term in the AP 15, ?, 23, 27, 31? (a) 23 (b) 20 (c) 18 (d) 19
  5. 5.What is the 10th term of the AP 16, 21, 26, 31, …? (a) 66 (b) 45 (c) 61 (d) 50
  6. 6.What is the sum of the first 5 terms of the AP 9, 12, 15, …? (a) 150 (b) 21 (c) 78 (d) 75
  7. 7.What is the sum of all the whole numbers from 1 to 30? (a) 450 (b) 465 (c) 930 (d) 435
  8. 8.What is the sum of the first 26 odd numbers (1 + 3 + 5 + …)? (a) 676 (b) 702 (c) 351 (d) 51
  9. 9.What is the missing term in the AP 9, 14, 19, ?, 29? (a) 29 (b) 25 (c) 24 (d) 23
  10. 10.What is the sum of all the whole numbers from 1 to 45? (a) 1036 (b) 990 (c) 2070 (d) 1035
  11. 11.What is the 14th term of the AP 7, 14, 21, 28, …? (a) 105 (b) 91 (c) 98 (d) 99
  12. 12.What is the 33rd term of the AP 20, 26, 32, 38, …? (a) 192 (b) 198 (c) 218 (d) 212
  13. 13.What is the sum of the first 7 terms of the AP 4, 5, 6, …? (a) 10 (b) 49 (c) 98 (d) 50
  14. 14.Which term of the AP 19, 27, 35, 43, … is 331? (a) 42nd (b) 40th (c) 41st (d) 39th
  15. 15.What is the sum of all the whole numbers from 1 to 44? (a) 990 (b) 1980 (c) 968 (d) 946
  16. 16.What is the 22nd term of the AP 13, 20, 27, 34, …? (a) 167 (b) 160 (c) 147 (d) 154
  17. 17.What is the 33rd term of the AP 2, 5, 8, 11, …? (a) 101 (b) 96 (c) 98 (d) 99
  18. 18.What is the sum of the first 6 terms of the AP 6, 12, 18, …? (a) 252 (b) 144 (c) 36 (d) 126
  19. 19.What is the sum of the first 8 terms of the AP 9, 15, 21, …? (a) 240 (b) 51 (c) 264 (d) 480
  20. 20.What is the sum of all the whole numbers from 1 to 75? (a) 2851 (b) 5700 (c) 2850 (d) 2775
  21. 21.What is the sum of the first 6 terms of the AP 1, 6, 11, …? (a) 26 (b) 162 (c) 81 (d) 96
  22. 22.What is the 22nd term of the AP 8, 12, 16, 20, …? (a) 84 (b) 88 (c) 92 (d) 96
  23. 23.Which term of the AP 9, 14, 19, 24, … is 124? (a) 25th (b) 24th (c) 26th (d) 23rd
  24. 24.What is the sum of the first 12 terms of the AP 2, 3, 4, …? (a) 96 (b) 90 (c) 13 (d) 180
  25. 25.Which term of the AP 16, 20, 24, 28, … is 128? (a) 28th (b) 32nd (c) 30th (d) 29th
  26. 26.What is the sum of the first 7 terms of the AP 8, 13, 18, …? (a) 38 (b) 322 (c) 161 (d) 166
  27. 27.What is the 18th term of the AP 11, 13, 15, 17, …? (a) 47 (b) 36 (c) 34 (d) 45
  28. 28.What is the sum of all the whole numbers from 1 to 51? (a) 1275 (b) 2652 (c) 1326 (d) 1327
  29. 29.What is the missing term in the AP 18, 27, ?, 45, 54? (a) 37 (b) 45 (c) 35 (d) 36
  30. 30.What is the 35th term of the AP 20, 26, 32, 38, …? (a) 210 (b) 204 (c) 224 (d) 230
  31. 31.What is the sum of the first 28 odd numbers (1 + 3 + 5 + …)? (a) 784 (b) 406 (c) 55 (d) 812
  32. 32.What is the 29th term of the AP 11, 18, 25, 32, …? (a) 203 (b) 207 (c) 214 (d) 196
  33. 33.What is the missing term in the AP 2, ?, 6, 8, 10? (a) 6 (b) 3 (c) 4 (d) 5
  34. 34.What is the missing term in the AP 1, ?, 13, 19, 25? (a) 13 (b) 6 (c) 7 (d) 8
  35. 35.What is the sum of the first 7 terms of the AP 1, 7, 13, …? (a) 133 (b) 154 (c) 266 (d) 37
  36. 36.What is the 27th term of the AP 11, 14, 17, 20, …? (a) 78 (b) 81 (c) 92 (d) 89
  37. 37.What is the 14th term of the AP 5, 9, 13, 17, …? (a) 61 (b) 56 (c) 57 (d) 52
  38. 38.What is the 14th term of the AP 4, 11, 18, 25, …? (a) 98 (b) 102 (c) 95 (d) 91
  39. 39.What is the sum of all the whole numbers from 1 to 66? (a) 4422 (b) 2178 (c) 2211 (d) 2145
  40. 40.What is the sum of the first 7 terms of the AP 4, 6, 8, …? (a) 77 (b) 140 (c) 70 (d) 16

Answer key

  1. 290
  2. 70
  3. 35
  4. 19
  5. 61
  6. 75
  7. 465
  8. 676
  9. 24
  10. 1035
  11. 98
  12. 212
  13. 49
  14. 40th
  15. 990
  16. 160
  17. 98
  18. 126
  19. 240
  20. 2850
  21. 81
  22. 92
  23. 24th
  24. 90
  25. 29th
  26. 161
  27. 45
  28. 1326
  29. 36
  30. 224
  31. 784
  32. 207
  33. 4
  34. 7
  35. 133
  36. 89
  37. 57
  38. 95
  39. 2211
  40. 70

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